Using PCR-TOPSIS to optimise Taguchi's multi-response problem

The Taguchi method is an efficient method used in off-line quality control where experimental design is combined with quality loss. This method includes three stages—system design, parameter design, and tolerance design. In the real world it is obvious that more than one quality characteristic should be considered for most industrial products; i.e., in most applications the customer's concern is with multi-response problems. Nevertheless, the Taguchi method is not appropriate for optimising a multi-response problem since engineering judgment is the main optimisation procedure in Taguchi method. In order to overcome this problem, this paper proposes an effective procedure called PCR-TOPSIS that is based on process capability ratio (PCR) theory and on the theory of order preference by similarity to the ideal solution (TOPSIS) to optimise multi-response problems. Using PCR-TOPSIS, multiple responses in each experiment will be transformed into a performance index. Therefore, the optimal factors/levels combinations for the multi-responses can be determined. Two case studies in Tarng et al. and Reddy et al. are resolved using the proposed procedure. The result indicates that PCR-TOPSIS can yield a satisfactory solution for multi-response problems.     

Optimum process conditions on shrinkage of an injected-molded part of DVD-ROM cover using Taguchi robust method

Plastic injection molding is an important process to produce thin-shell parts. However, the difficulty in adjusting optimum process conditions may cause defects of the injected-molded parts such as shrinkage. This study investigates on the optimum combinations of process conditions on shrinkage of an injected-molded part of the DVD-ROM cover based on Taguchi method. In doing this, a series of Moldflow analyses have been performed as per L₂₇ orthogonal array design with each analysis by means of the process conditions of mold temperature, melt temperature, injection pressure, injection time, and cooling time. In the meantime, signal-to-noise (S/N) ratio is utilized to determine the optimum combinations of the process conditions for shrinkage through analysis of variance (ANOVA). ANOVA is further used to find which of the process conditions are statistically significant. Finally, confirmation tests at the optimum combinations of the process conditions were executed to verify the robustness and the effectiveness of Taguchi method within 95% confidence interval. From the findings, it can be stated that Taguchi method is a powerful tool for evaluating the defect of shrinkage in the plastic injection molding.     

An integrated parameter optimization system for MISO plastic injection molding

This paper presents the development of a parameter optimization system that integrates mold flow analysis, the Taguchi method, analysis of variance (ANOVA), back-propagation neural networks (BPNNs), genetic algorithms (GAs), and the Davidon–Fletcher–Powell (DFP) method to generate optimal process parameter settings for multiple-input single-output plastic injection molding. In the computer-aided engineering simulations, Moldex3D software was employed to determine the preliminary process parameter settings. For process parameter optimization, an L₂₅ orthogonal array experiment was conducted to arrange the number of experimental runs. The injection time, velocity pressure switch position, packing pressure, and injection velocity were employed as process control parameters, with product weight as the target quality. The significant process parameters influencing the product weight and the signal to noise (S/N) ratio were determined using experimental data based on the ANOVA method. Experimental data from the Taguchi method were used to train and test the BPNNs. Then, the BPNN was combined with the DFP method and the GAs to determine the final optimal parameter settings. Three confirmation experiments were performed to verify the effectiveness of the proposed system. Experimental results show that the proposed system not only avoids shortcomings inherent in the commonly used Taguchi method but also produced significant quality and cost advantages.     

Machining Characteristics of Al2O3/6061Al Composite using Rotary EDM with a Disklike Electrode

This work optimises the cutting of Al₂O₃/6061Al composite using rotary electro-discharging machining (EDM) with a disklike electrode by using Taguchi methodology. The Taguchi method is used to formulate the experimental layout, to analyse the effect of each EDM parameter on the machining characteristics, and to predict the optimal choice for each EDM parameter. Four observed values, MRR, EWR, REWR, and SR, are used to verify this optimisation of the machining technique. In addition, six independent parameters are chosen as variables in evaluating the Taguchi method and are categorised into two groups: 1. Electrical parameters, e.g. polarity, peak current, pulse duration, and powder supply voltage. 2. Non-electrical parameters, e.g. circumferential speed of electrode, reciprocating speed. The analysis of the Taguchi method reveals that, in general, the electrical group more significantly affects the machining characteristics than the non-electrical group. Also derived herein are semi-empirical equation that contain all of the machining characteristics. Experimental results are presented to illustrate the proposed approach.     

Multi-response optimisation of WEDM process using principal component analysis

Like many other processes, the wire electrical discharge machining (WEDM) process has several performance characteristics. Determination of the optimal process settings with respect to all these performance measures (responses) is an important issue. Taguchi’s robust design method can only be applied to optimise a single-response problem. Some researchers have attempted to optimise WEDM operations using a multi-response signal-to-noise (MRSN) ratio and constraint optimisation methods. Both these methods suffer from some weaknesses. The principal component analysis (PCA)-based approach for multi-response optimisation can effectively overcome those weaknesses. In this paper, some modifications in the PCA-based approach are suggested and two sets of experimental data published by the past researchers are analysed using this modified procedure. It is observed that the PCA-based optimisation can give better results than the constrained optimisation and MRSN ratio-based methods, which can be attributed to the fact that the possible correlation among the multiple responses is taken care in the PCA-based approach.     

Optimization of brazing conditions for OFHC Cu and ASTM A501 low carbon steel by taguchi method

This paper concerns the optimization of brazing conditions for joining the two dissimilar materials Oxygen-free high conductivity (OFHC) copper and ASTM A501 low carbon steel usually used for an Oil-Separator of an air-conditioner using Ag-based (BAg) alloy as a brazing filler metal (BFM). A mixture of 70% N₂ and 30% H₂ gases was used to prevent oxidation of the joints during furnace brazing process. Brazing joint clearance, length, temperature, and time were selected as design parameters that have significant effect on the bonding strength of a brazed joint. Taguchi method was used as a statistical technique for design of experiment (DOE) in an attempt to optimize brazing conditions in terms of shear strength. L₉ (3⁴) orthogonal array was designed for conducting the experiments. The relative influence of design parameters and their interaction on the response were also discussed. The experimental results verified that the brazing conditions predicted in this study by Taguchi method could produce the brazed joint between OFHC copper and ASTM A501 low carbon steel with maximum shear strength.     

Optimisation of multiple responses for WEDM processes using weighted principal components

Taguchi method is widely used for optimisation of various processes. Using Taguchi method, the parametric settings can be optimised with respect to one performance characteristic (response) at a time, whereas wire electrical discharge machining (WEDM) processes require optimisation of multiple performance characteristics. Researchers have attempted several approaches but determination of the optimal process settings that can optimise multiple performance measures (responses) of WEDM operations still remains an important issue. In this paper, weighted principal component (WPC) method is used to optimise the multiple responses of WEDM processes. The results show that the WPC method offers significantly better overall quality than the other approaches.     

The principal component analysis (PCA)-based approaches for multi-response optimization: some areas of concerns

Over the years, Taguchi method for process optimisation has become very popular among the engineers. However, Taguchi method focuses on the optimisation of a single-response variable only, whereas most of the modern manufacturing processes demand for simultaneous optimisation of multiple response variables, and some of these responses are often correlated. Several methods have been proposed in literature which aims at making the Taguchi method useful for solving multi-response optimisation problems too. However, only few of these methods take into account the possible correlations that may exist among the response variables. Among these, principal component analysis (PCA)-based approaches are quite popular among the practitioners. However, we find that the PCA-based approaches suffer from some weaknesses, e.g. problem due to using signal-to-noise ratios as input data, problem due to scaling of the input data, problem due to difference in PCA results given by different software. This article aims at drawing attention of the researchers/practitioners to these problem areas of the PCA-based approaches so that appropriate research initiatives can be taken up by the researchers/practitioners to overcome those weaknesses.     

Taguchi-based Six Sigma approach to optimize plasma cutting process: an industrial case study

This case study outlines the use of Taguchi parameter design to optimize the roundness of holes made by an aging plasma-cutting machine. An L₉ array is used in a Taguchi experiment design consisting of four controllable factors, each with three levels. With two non-controllable factors included in the setting, we conduct 36 experiments, compared to the 81 parameter combinations (four factors, three levels or 3⁴) required in a traditional DOE setting. Therefore, using the Taguchi method significantly reduces the time and costs of a quality improvement process. Conducted for two response variables—bevel magnitude and the smallest diameter deviation of the hole—the Taguchi experiments gave the optimal combination A₁B₂C₁D₃ (small for tip size, 93 in/min for feed rate, 100 V for voltage, and 63A for amperage), which is verified with a confirmation run of 30 work pieces. All 30 cuts meet the quality requirement for subsequent assembly. Furthermore, statistical analysis indicates that the mean value and standard deviation of the confirmation run data are smaller than those before Taguchi parameter design is conducted.     

Optimization of flux-cored arc welding process parameters by using genetic algorithm

The effect of flux-cored arc welding (FCAW) process parameters on the quality of the super duplex stainless steel (SDSS) claddings can be studied using Taguchi L9 design of experiments. In this experimental investigation, deposits were made with 30 % bead overlap. Establishing the optimum combination of process parameters is required to ensure better bead geometry and desired properties. The above objectives can be achieved by identifying the significant input process parameters as input to the mathematical models like welding voltage (X ₁), wire feed rate (X ₂), welding speed (X ₃), and nozzle-to-plate distance (X ₄). The identified responses governing the bead geometry are bead width (W) and height of the reinforcement (H). The mathematical models were constructed using the data collected from the experiments based on Taguchi L9 orthogonal array. Then, the responses were optimized using non-traditional nature-inspired technique like genetic algorithm (GA).     

Optimization of degree of sphericity of primary phase during cooling slope casting of A356 Al alloy: Taguchi method and regression analysis

The present work presents the results of experimental investigation of semi-solid rheocasting of A356 Al alloy using a cooling slope. The experiments have been carried out following Taguchi method of parameter design (orthogonal array of L₉ experiments). Four key process variables (slope angle, pouring temperature, wall temperature, and length of travel of the melt) at three different levels have been considered for the present experimentation. Regression analysis and analysis of variance (ANOVA) has also been performed to develop a mathematical model for degree of sphericity evolution of primary α-Al phase and to find the significance and percentage contribution of each process variable towards the final outcome of degree of sphericity, respectively. The best processing condition has been identified for optimum degree of sphericity (0.83) as A₃, B₃, C₂, D₁ i.e., slope angle of 60°, pouring temperature of 650 °C, wall temperature 60 °C, and 500 mm length of travel of the melt, based on mean response and signal to noise ratio (SNR). ANOVA results shows that the length of travel has maximum impact on degree of sphericity evolution. The predicted sphericity obtained from the developed regression model and the values obtained experimentally are found to be in good agreement with each other. The sphericity values obtained from confirmation experiment, performed at 95% confidence level, ensures that the optimum result is correct and also the confirmation experiment values are within permissible limits.     

A neural network solution for LOM process performance

A neural network (NN) modeling approach is presented for the prediction of laminated object manufacturing (LOM) process performance. A NN was developed using experimental data which were conducted on a LOM 1015 machine according to the principles of Taguchi design of experiments (DoE) method. The process parameters considered in the experiment to investigate LOM process performance were nominal layer thickness (NLT), heater temperature (HT), platform retract (PR), heater speed (HS), laser speed (LS), feeder speed (FS), and platform speed (PS). LOM process performance is divided in dimensional errors in X and Y directions (Ex and Ey), actual layer thickness (ALT), average surface roughness of vertical supporting frame (VSF-R_a), and tensile strength in X direction (TSx). It was found that NN approach can be applied in an easy way on designed experiments and predictions can be achieved, fast and quite accurate. The developed NN is constrained by the experimental region in which the designed experiment is conducted. Thus, it is very important to select parameters’ levels as well as the limits of the experimental region and the structure of the orthogonal experiment. The above analysis is useful for LOM users when prediction of process performance is needed. This methodology could be easily applied to different materials and initial conditions for optimization of other Rapid Prototyping (RP) processes.     

Establishing process parameter levels for double-sided PCBs

This study deals with establishing an initial manufacturing process for a denser printed circuit board compared to the existing ones. The increase in the density resulted in an increased level of rejection due to short and open circuits in the existing process. To maximize the proportion of nondefective circuits for denser board, an experiment involving a two-level factor and seven three-level factors was planned. Taguchi’s L ₁₈ orthogonal array was used to design the experiment. A second-order linear logistic model adequately represented the logit of the proportion of nondefective circuits over the zone of exploration. A constrained nonlinear optimization technique yielded an optimum process parameter setting that resulted in about 82% circuits being free from shorts and opens. A confirmatory trial based on the optimum process parameter levels corroborated the findings of the study.     

Uniformity and signal-to-noise ratio for static and dynamic parameter designs of deposition processes

In this paper, the relationship between the uniformity measure (U) and the Taguchi signal-to-noise ratio (SNR) for parameter design (or robust design) is investigated with a focus on the deposition process. For the static parameter design, it can be easily shown that U is directly related to the Taguchi SNR, and, as such, U can be interpreted as a measure directly related to the expected loss after the mean thickness is adjusted to the target. For the dynamic parameter design in which the target of a characteristic (e.g., the target thickness for a deposition process) changes, the Taguchi SNR is conditional on the signal parameter values (e.g., the deposition times) used in the parameter design experiment. Therefore, a new performance measure is developed considering a general distribution of the target thickness, and it is shown that U is also equivalent to this new performance measure. In summary, U can be used as a valid performance measure for the dynamic as well as static parameter design of a deposition process. Based on these findings, static and dynamic parameter design procedures for a deposition process are developed considering not only U but also the deposition rate, and the proposed dynamic procedure is illustrated with an example case study.     

Optimization of cutting parameters on drill bit temperature in drilling by Taguchi method

In this study, the optimization of the cutting parameters on drill bit temperature in drilling was performed. Al 7075 work piece and the uncoated and Firex® coated carbide drills in the experimental were used. The optimization of the cutting parameters was evaluated by Taguchi method. The control factors were considered as the cutting speed, feed rate and cutting tool. Taguchi method was used to determining the settings of cutting parameters. The L₁₈ orthogonal array was used in experimental planning. The most significant control factors affected on drill bit temperature measurements was obtained by using analysis of variance (ANOVA). Taguchi design method exhibit a good performance in the optimization of cutting parameters on drill bit temperature measurements. In addition, the empirical equations of drill bit temperatures were derived by using regression analysis. The obtained equations results compared with the drill bit temperature measurement results. The empirical equations results indicated a good agreement with experimental results.     

A study of the Taguchi optimization method for surface roughness in finish milling of mold surfaces

The objective of this paper is to develop a Taguchi optimization method for low surface roughness in terms of process parameters when milling the mold surfaces of 7075-T6 aluminum material. Considering the process parameters of feed, cutting speed, axial-radial depth of cut, and machining tolerance, a series of milling experiments were performed to measure the roughness data. A regression analysis was applied to determine the fitness of data used in the Taguchi optimization method using milling experiments based on a full factorial design. Taguchi orthogonal arrays, signal-to-noise (S/N) ratio, and analysis of variance (ANOVA) are used to find the optimal levels and the effect of the process parameters on surface roughness. A confirmation experiment with the optimal levels of process parameters was carried out in order to demonstrate the effectiveness of the Taguchi method. It can be concluded that Taguchi method is very suitable in solving the surface quality problem of mold surfaces.     

Determining the optimum process parameter for grinding operations using robust process

We applied combined response surface methodology (RSM) and Taguchi methodology (TM) to determine optimum parameters for minimum surface roughness (Ra) and vibration (Vb) in external cylindrical grinding. First, an experiment was conducted in a CNC cylindrical grinding machine. The TM using L ₂₇ orthogonal array was applied to the design of the experiment. The three input parameters were workpiece revolution, feed rate and depth of cut; the outputs were vibrations and surface roughness. Second, to minimize wheel vibration and surface roughness, two optimized models were developed using computer-aided single-objective optimization. The experimental and statistical results revealed that the most significant grinding parameter for surface roughness and vibration is workpiece revolution followed by the depth of cut. The predicted values and measured values were fairly close, which indicates (R _Ra ² =94.99 and R _Vb ² =92.73) that the developed models can be effectively used to predict surface roughness and vibration in the grinding. The established model for determination of optimal operating conditions shows that a hybrid approach can lead to success of a robust process.     

Optimising the thermoforming process of polymeric foams: an approach by using the Taguchi method and the utility concept

The use of the conventional Taguchi method for determining the optimum setting of controllable factors through off-line experiments focuses on products with a single quality characteristic or response. However, most products have several qualitative characteristics or responses of interest. The Taguchi method in itself optimises a single response or performance characteristic, yielding a set of process parameters. This particular setting, however, may not give the desired results for other characteristics of the product. There is a need to obtain a single optimum setting of process parameters that can be used to produce products with optimum or near optimum quality characteristics as a whole. Multi-characteristic response optimisation may be the solution to the above problem. In this report, a case study on thermoforming polypropylene foams, utilising a simplified multi-criterion methodology based on Taguchis approach and utility concept, is discussed. Key processing factors affecting product quality are identified. It has been shown that the proposed Taguchi approach with the utility concept can provide an appropriate solution to yield a satisfactory product quality for a multi-response process optimisation problem.     

Optimum selection of abrasive flow machining conditions during fine finishing of Al/15 wt% SiC-MMC using Taguchi method

Abrasive flow machining (AFM) is gaining widespread application finishing process on difficult to reach surfaces in aviation, automobile, and tooling industry. Al/SiC_p-MMC is a promising material in these industries. Here, AFM has been used to finish conventionally machined cylindrical surface of Al/15 wt% SiC_p-MMC workpiece. This paper presents the utilization of robust design-based Taguchi method for optimization of AFM parameters. The influences of AFM process parameters on surface finish and material removal have been analyzed. Taguchi experimental design concept, L₁₈ (6¹?×?3⁷) mixed orthogonal array is used to determine the S/N ratio and optimize the AFM process parameters. Analysis of variance and F test values also indicates the significant AFM parameters affecting the finishing performance. The mathematical models for R _a, R _t, ΔR _a, and ΔR _t and material removal are established to investigate the influence of AFM parameters. Conformation test results verify the effectiveness of these models and optimal parametric combination within the considered range. Scanning electron micrographs testifies the effectiveness of AFM process in fine finishing of Al/15 wt% SiC_p-MMC.     

Process improvement in laser hot wire cladding for martensitic stainless steel based on the Taguchi method

Laser hot wire cladding, with the prominent features of low heat input, high energy efficiency, and high precision, is widely used for remanufacturing metal parts. The cladding process, however, needs to be improved by using a quantitative method. In this work, volumetric defect ratio was proposed as the criterion to describe the integrity of forming quality for cladding layers. Laser deposition experiments with FV520B, one of martensitic stainless steels, were designed by using the Taguchi method. Four process variables, namely, laser power (P), scanning speed (V _s), wire feed rate (V _f), and wire current (I), were optimized based on the analysis of signal-to-noise (S/N) ratio. Metallurgic observation of cladding layer was conducted to compare the forming quality and to validate the analysis method. A stable and continuous process with the optimum parameter combination produced uniform microstructure with minimal defects and cracks, which resulted in a good metallurgical bonding interface.